Date: Thursday, November 10, 2016
Location: B844 East Hall (3:10 PM to 4:00 PM)
Title: On the unirationality of M_{1,n} in characteristic p.
Abstract: We show that the DeligneMumford moduli space of genus 1 curves with n marked points is not unirational in characteristic p, for n sufficiently large with respect to p, when p>7. This statement, as well as the nonunirationality of many other DeligneMumford moduli spaces, was wellknown in characteristic zero, but is more difficult in characteristic p. Our method uses the action of Frobenius on the etale cohomology of M_{1,n}. Following Deligne, we can compute this cohomology in terms of modular forms. The unirationality then follows from classical results on modular forms modulo p.
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Speaker: Will Sawin
Institution: Princeton/ETH
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